Geodesic
On Log Q-Homology Planes and Weighted Projective Planes
Canadian journal of mathematics, Tome 56 (2004) no. 6, pp. 1145-1189

Voir la notice de l'article provenant de la source Cambridge University Press

We classify normal affine surfaces with trivial Makar-Limanov invariant and finite Picard group of the smooth locus, realizing them as open subsets of weighted projective planes. We also show that such a surface admits, up to conjugacy, one or two ${{G}_{a}}$ -actions.
DOI : 10.4153/CJM-2004-051-9
Mots-clés : 14R05, 14J26, 14R20 
Daigle, Daniel; Russell, Peter. On Log Q-Homology Planes and Weighted Projective Planes. Canadian journal of mathematics, Tome 56 (2004) no. 6, pp. 1145-1189. doi: 10.4153/CJM-2004-051-9
@article{10_4153_CJM_2004_051_9,
     author = {Daigle, Daniel and Russell, Peter},
     title = {On {Log} {Q-Homology} {Planes} and {Weighted} {Projective} {Planes}},
     journal = {Canadian journal of mathematics},
     pages = {1145--1189},
     year = {2004},
     volume = {56},
     number = {6},
     doi = {10.4153/CJM-2004-051-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2004-051-9/}
}
TY  - JOUR
AU  - Daigle, Daniel
AU  - Russell, Peter
TI  - On Log Q-Homology Planes and Weighted Projective Planes
JO  - Canadian journal of mathematics
PY  - 2004
SP  - 1145
EP  - 1189
VL  - 56
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2004-051-9/
DO  - 10.4153/CJM-2004-051-9
ID  - 10_4153_CJM_2004_051_9
ER  - 
%0 Journal Article
%A Daigle, Daniel
%A Russell, Peter
%T On Log Q-Homology Planes and Weighted Projective Planes
%J Canadian journal of mathematics
%D 2004
%P 1145-1189
%V 56
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2004-051-9/
%R 10.4153/CJM-2004-051-9
%F 10_4153_CJM_2004_051_9

[1] [1] Bandman, T. and Makar-Limanov, L., Affine surfaces with AK(S) = (C. Michigan Math. J. 49(2001), 567–582. Google Scholar

[2] [2] Bertin, J., Pinceaux de droites et automorphismes des surfaces affines. J. Reine Angew.Math. 341(1983), 32–53. Google Scholar

[3] [3] Daigle, D., Classification of weighted graphs up to blowing-up and blowing-down, arXiv:math.AG/0305029. Google Scholar

[4] [4] Daigle, D., Homogeneous locally nilpotent derivations of k[x, y, z]. J. Pure Appl. Algebra 128(1998), 109–132. Google Scholar

[5] [5] Daigle, D. and Russell, P., Affine rulings of normal rational surfaces, Osaka J.Math. 38(2001), 37–100. Google Scholar

[6] [6] Daigle, D. and Russell, P., On weighted projective planes and their affine rulings. Osaka J. Math. 38(2001), 101–150. Google Scholar

[7] [7] Fieseler, Karl-Heinz, On complex affine surfaces with (C+-action. Comment. Math. Helvetici 69(1994), 5–27. Google Scholar

[8] [8] Gizatullin, M.H., Invariants of incomplete algebraic surfaces that can be obtained by means of completions. Izv. Akad. Nauk SSSR Ser.Mat. 35(1971), 485–497. Google Scholar

[9] [9] Gizatullin, M.H., Quasihomogeneous affine surfaces. Izv. Akad. Nauk SSSR Ser.Mat. 35(1971), 1047–1071. Google Scholar

[10] [10] Gurjar, R.V., Miyanishi, M., On the Makar-Limanov invariant and fundamental group at infinity. Preprint, 2002. Google Scholar

[11] [11] Masuda, K. and Miyanishi, M.,The additive group actions on ℚ-homology planes. Ann. Inst. Fourier (Grenoble) 53(2003), 429–464. Google Scholar

[12] [12] Rentschler, R., Opérations du groupe additif sur le plan affine, C. R. Acad. Sci. Paris 267(1968), 384–387. Google Scholar

[13] [13] Shastri, A.R., Divisors with finite local fundamental group on a surface. In: Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 46, American Mathematical Society, Providence, RI, 1987, pp. 467–481. Google Scholar

[14] [14] Yoshihara, H., On Plane Rational Curves. Proc. Japan Acad. (Ser A) 55(1979), 152–155. 55(1979), 152–155. Google Scholar

Cité par Sources :